The present invention relates generally to positioning and navigation systems that use the Global Positioning System (GPS), and particularly to carrier phase signal integer ambiguity resolution for high accuracy real-time positioning and navigation with satellite-based navigation systems.
Currently, three types of GPS measurements corresponding to each correlator channel with a locked GPS satellite signal are available for civilian GPS receivers. The three types of GPS measurements are pseudorange, Doppler, and integrated carrier phase for two carrier frequencies, L1 and L2. See Farrell, J. A. and Barth, M., The Global Positioning System and Inertial Navigation, McGraw-Hill (ISBN-0-07-022045-X), 1999, hereby incorporated by reference. GPS Integer ambiguity resolution is a key issue in high accuracy positioning and navigation using carrier phase measurements. The objective of GPS integer ambiguity resolution is to solve for the integer number of complete carrier cycles during transmission of a GPS signal from the GPS satellite to a receiver, or the difference between the integer number of complete carrier cycles from the GPS satellite to a reference receiver and that from the GPS satellite to a user receiver.
GPS applications, whether they are short range or long range, static positioning or dynamic/kinematic positioning, whether they involve real-time processing or post processing, known or unknown baseline, all require GPS integer ambiguity resolution for high accuracy performance. In practical applications, GPS carrier phase integer ambiguity resolution is usually accomplished in two steps: (1) solving for the integer ambiguity using special search and hypothesis testing techniques; and (2) verifying that the integer ambiguity solution is unique and correct.
Three categories of methods have been developed to solve and validate the integer ambiguity. The first category of methods is based on long duration static observation. These methods are typically used in static mode where the position of the GPS receiver does not change for a long duration of time, so that long time observation data can be used to reduce errors caused by multipath and GPS receiver noise, and to allow the GPS satellites to make significant changes in position during the position determining process. See Remondi, B. W., xe2x80x9cKinematic and Pseudo-Kinematic GPS,xe2x80x9d Proceeding of the Satellite Division of the Institute of Navigation First International Technical Meeting, Colorado Springs, Colo., Sep. 21-23, 1988, hereby incorporated by reference.
The second category of methods requires special moving of GPS antennae, such as GPS antennae swapping as described by Remondi, B. W., xe2x80x9cPerforming Centimeter-Level Surveys in Seconds with GPS Carrier Phase: Initial Results,xe2x80x9d Journal of The Institute of Navigation, Vol. 32, No. 4, Winter 1985-1986, hereby incorporated by reference. Swapping location of two antennae causes rapid change in the observability of the GPS receiver position, but is rarely possible in real-time kinematic applications.
The above two categories of methods are straightforward but require special assumptions and conditions that may not be practical for specific applications. The third category of methods includes searching methods that require fewer assumptions, such as:
the ambiguity function method described by Counselman, C. and Gourevitach S., xe2x80x9cMiniature Intergerometer Terminals for Earth Surveying: Ambiguity and Multipath with the Global Position System,xe2x80x9d IEEE Transactions on Geoscience and Remote Sensing, GE-19(4): 244-252, 1981;
the fast ambiguity resolution approach described by Frei, E. and G. Beutler, xe2x80x9cRapid Static Positioning Based on the Fast Ambiguity Resolution Approach FARA: Theory and First Results,xe2x80x9d Manuscripts Geodaetia, 1990, pp.325-356;
the least squares ambiguity search technique described by Hatch, R. R., xe2x80x9cInstantaneous Ambiguity Resolution,xe2x80x9d Kinematic Systems in Geodesy, Surveying and Remote Sensing, IAG Symposia 107, Springer Verlag, N.Y., September, 1990, pp. 299-308, and by Farrell, J. A. and Barth, M, supra;
the Cholesky decomposition method in Landau, H. and Euler, H. J., xe2x80x9cOn-The-Fly Ambiguity Resolution for Precise Differential Positioning,xe2x80x9d Processing of ION GPS-92, Albuquerque, N.Mex., 16-18 Sep., 1992, pp. 607-613;
the fast ambiguity search filter described by Chen, D., xe2x80x9cFast Ambiguity Search Filter (FASF): A Novel Concept from GPA Ambiguity Resolution,xe2x80x9d Processing of the ION GPS-93, Salt Lake City, Utah, Sep. 22-24, 1993, pp. 781-787; and
the least squares ambiguity decorrelation adjustment method by Teunissen, P. J. G., xe2x80x9cA New Method for Fast Carrier Phase Ambiguity Estimation,xe2x80x9d Proceedings IEEE Position Location and Navigation Symposium PLAN94, Las Vegas, 11-15 Apr., 1994, pp. 562-573.
All of the publications cited above are hereby incorporated by reference as background information.
Searching methods for solving integer ambiguity in GPS applications face many issues, including linear stochastic model definition, ambiguity resolution initialization, search space reduction, state and standard deviation calculation in the search space, and validation and rejection criteria for the unique and correct candidate. Among these, search space reduction is critically important. The purpose of search space reduction is to reduce the number of integer candidates (or the size of a search space) for the carrier phase integers without missing the correct candidates. The size of the search space not only affects how fast an ambiguity resolution method solves for the carrier phase integers (i.e., the carrier phase integer for each GPS signal), but also determines the success rate of the ambiguity resolution method. Usually, the smaller the search space, the easier it is to find a unique and correct candidate set for the carrier phase integers.
One approach to reduce the search space is to decrease diagonal element values of a covariance matrix that determines the search space. See Teunissen, P. J. G., supra. Existing methods to decrease diagonal element values of the covariance matrix include: improving the GPS receiver measurement performance; in a dual frequency GPS receiver, combining L1 and L2 measurements to suppress pseudorange measurement noise, or using phase smoothing code (such as a Hatch filter) to reduce the measurement noise; and applying an integer inverse matrix transformation to decorrelate the double differential measurement and to reduce integer ambiguity covariance element values.
Another approach to reduce the search space is to increase the length of the search steps by using a longer wavelength (e.g., by combining the L1 and L2 phases). However, using a longer wavelength usually means increased measurement noise.
Furthermore, the search space can be greatly reduced by cutting search dimensions determined by the number of satellites used for GPS measurements. Cutting the search dimensions can greatly reduce the number of searching candidates. For example, if each search range includes 10 search cycles, to resolve the ambiguities of four carrier phase integers the total number of candidate sets for the four carrier phase integers is 104, while to resolve the ambiguities of seven carrier phase integers, the total number of candidate sets is 107. Therefore, in some search methods, the differential GPS measurements are partitioned into a primary measurement set and a secondary measurement set. The phase measurements of the primary set define the reduced search space, while the phase measurements of the secondary set are used to verify the correctness of the resolved candidates. See Hatch, R. R., xe2x80x9cInstantaneous Ambiguity Resolution,xe2x80x9d Supra.
The present invention includes a method of fast GPS carrier phase integer ambiguity resolution, based on properties of a Residual Sensitivity Matrix (S matrix), which directly relates a set of integer ambiguities to carrier phase residuals. In one embodiment of the present invention, the method uses the Singular Value Decomposition of the S Matrix to split the integer ambiguity set into two integer ambiguity subsets and to derive a relationship between the two integer ambiguity subsets. Thus, searching for the integer ambiguity set is reduced to searching for one of the two integer ambiguity subsets, resulting in a greatly reduced search space. In an alternative embodiment of the present invention, splitting the integer ambiguity set into two integer ambiguity subsets and deriving a relationship between the two integer ambiguity subsets are accomplished by selecting a portion of the rows of the S matrix as linearly independent rows of the S matrix and rearranging the S matrix according to the selection. The rearranged S matrix is then split into four sub-matrices, which are used to relate the two integer ambiguity subsets.
The searched integer ambiguity subset can be selected from the integer ambiguity set based on, or taking into consideration, the satellite geometry and measurement residuals. As a result, the method of the present invention not only improves the calculation efficiency and ambiguity resolution time, but also improves the reliability of the search result.